Related papers: Convergence rates for an Adaptive Biasing Potentia…
Ensuring a satisfactory statistical convergence of anharmonic thermodynamic properties requires sampling of many atomic configurations, however the methods to obtain those necessarily produce correlated samples, thereby reducing the…
The computational costs of inference and planning have confined Bayesian model-based reinforcement learning to one of two dismal fates: powerful Bayes-adaptive planning but only for simplistic models, or powerful, Bayesian non-parametric…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to…
We consider minimizing finite-sum and expectation objective functions via Hessian-averaging based subsampled Newton methods. These methods allow for gradient inexactness and have fixed per-iteration Hessian approximation costs. The recent…
Constrained sampling is an important and challenging task in computational statistics, concerned with generating samples from a distribution under certain constraints. There are numerous types of algorithm aimed at this task, ranging from…
The goal of this paper is to explore the basic Approximate Bayesian Computation (ABC) algorithm via the lens of information theory. ABC is a widely used algorithm in cases where the likelihood of the data is hard to work with or…
This article is a companion paper to our earlier work Miroshnikov et al. (2021) on fairness interpretability, which introduces bias explanations. In the current work, we propose a bias mitigation methodology based upon the construction of…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting…
We study the quantitative convergence of drift-diffusion PDEs that arise as Wasserstein gradient flows of linearly convex functions over the space of probability measures on ${\mathbb R}^d$. In this setting, the objective is in general not…
Variational inference in probabilistic graphical models aims to approximate fundamental quantities such as marginal distributions and the partition function. Popular approaches are the Bethe approximation, tree-reweighted, and other types…
Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…
This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing…
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method can be seen as an adequate…
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic…
In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and essentially provides a convergent variant of the Barzilai-Borwein method for…